Calculating avg hit on landing WS

[eva00r]

Normally I use Studio Gobli (JP website) to calculate how many hits I am going to land WS with each setup. But right now it's broken so I'd like to know the math formular so I can calculate it with my Excel.

The website took these variable and displayed this kind of result.
1) # of attacks in WS [1-8] e.g. 4 for vorpal, 5 for rampage, 8 for asuran
2) Your accuracy x%
3) Double Attack y%
4) Triple Attack z%

Expected Result
8 hits 0%
7 hits 1%
6 hits 5%
5 hits 60%
4 hits 30%
3 hits 10%
2 hits 3%
1 hit 1%

May you guys can help with some math and excel formula ^^

[diemos]

VZX where you at?

http://www.freewebs.com/vzx-01/

[VZX]

Ask Ruke,
I'm not so sure about overlapping double/triple attack

[eva00r]

Com'on anyone offer me some help please?

[nivlakian]

Since no one has answered, I can help to get you started in setting up an equation, but I don't really know the rules for how many double attacks are allowed and on what hits etc.

N = number of hits to actually connect
H = number of hits in WS
A = accuracy% as a decimal
D = double attack % as a decimal
T = triple attack % as a decimal

Chance to get N hits without taking into account that double or triple attack can occur:
nCr(H, N) * A^N * (1-A)^(H-N)

Chance to get N hits if no double or triple attack happens:
nCr(H, N) * A^N * (1-A)^(H-N) * (1-D)^H * (1-T)^H

Chance to get N hits if 1 double attack happens, but no triple attack:
nCr(H, N) * A^N * (1-A)^(H-N) * (1-D)^H * (1-T)^H +
nCr(H, N-1) * A^N * (1-A)^(H-N) * nCr(N,1) * D * (1-T)^H

Chance to get N hits if 1 triple attack happens, but no double attack:
nCr(H, N) * A^N * (1-A)^(H-N) * (1-D)^H * (1-T)^H +
nCr(H, N-2) * A^N * (1-A)^(H-N) * nCr(N,1) * T * (1-D)^H

Chance to get N hits if 1 triple attack happens OR 1 double attack:
nCr(H, N) * A^N * (1-A)^(H-N) * (1-D)^H * (1-T)^H +
nCr(H, N-1) * A^N * (1-A)^(H-N) * nCr(N,1) * D * (1-T)^H +
nCr(H, N-2) * A^N * (1-A)^(H-N) * nCr(N,1) * T * (1-D)^H

The ones where I attempted to take into account double attack and triple attack may not be completely right, but perhaps someone will come to correct it.

[VZX]

The deal is double attack and triple attack can't proc on a single swing.
Do they share the same percentage with single swing proc?
If so, how you make 75% 2A and 75% 3A (I know, just a hypothetical number, but still don't break the rule. If there's any) on 1000 swings outcome look like?

If they don't share the same percentage, which one will be activated first? 3A? or 2A? (if in the roll both triggers on the same round)

EDIT : changed round -> swing

[Suiram]

I was thinking about this yesterday, and the best approach I could come up with is this: Break the function P(k,m,A,D,T) (the probability of landing k hits in an m-hit WS with Accuracy A%, DA rate D%, and TA rate T%) into two functions, S(n,m,D,T) and L(k,n,A).

L is niv's first formula, the chance of landing k hits in n swings with A% accuracy.
L(k,n,A) = C(n,k) * A^k * (1-A)^(n-k)

S is going to be tougher, and when I was trying to work it out yesterday I got distracted and never posted lol It's also going to depend on the hypotheses you have about DAs and TAs but it should be the probability of swinging n times on an m-hit WS with D% DA rate and T% TA rate. There are a few disputed or unknown elements of this:

• Can DA or TA proc on any secondary swings in a WS?[/*:m:32m5m69z]
• If DA or TA can proc on any swing, can it proc again a second or third time?[/*:m:32m5m69z]
• Is DA checked before TA on a given swing in the WS, or TA before DA, or do they have some sort of shared likelihood where one does not affect the other?[/*:m:32m5m69z]
• If multiple DAs/TAs can proc on a WS, can a TA proc on the 7th swing of a WS and be reduced to a DA due to the 8-swing cap, or is it prevented altogether?[/*:m:32m5m69z]

There are probably a couple more issues that would need to be decided. Also you have to take into account when building S that there's the 8-swing cap, so if you allow for multiple DAs/TAs you need to combine all of the chances for 8 and above into the probability of 8 swings. Anyway, once S is decided, then the overall formula, P(k,m,A,D,T), should be just:

The summation from n=m to 8 of [S(n,m,D,T) * L(k,n,A)]

[eva00r]

To speed things up, let me answer some of your questions.

Can DA or TA proc on any secondary swings in a WS?
- DA can proc on any secondary swings in a WS. Once in a while my NIN's Jin gives 6 hits TP return. (DA procs 3 times in 3 swings)
- I assume TA should be the same

If DA or TA can proc on any swing, can it proc again a second or third time?
- Yes, DA procs 3 times in 3 Jin's swings = 6 hits TP return.

Is DA checked before TA on a given swing in the WS, or TA before DA, or do they have some sort of shared likelihood where one does not affect the other?
- I don't know.

If multiple DAs/TAs can proc on a WS, can a TA proc on the 7th swing of a WS and be reduced to a DA due to the 8-swing cap, or is it prevented altogether?
- I don't exactly know how it works but I am strongly believe that it follows 8-swing cap rule. Or else some THFs will show up and yell that my Dancing Edge/Evisceration can hit more than 8 times.

[Kirschy]

To speed things up, let me answer some of your questions.

Can DA or TA proc on any secondary swings in a WS?
- DA can proc on any secondary swings in a WS. Once in a while my NIN's Jin gives 6 hits TP return. (DA procs 3 times in 3 swings)
- I assume TA should be the same

If DA or TA can proc on any swing, can it proc again a second or third time?
- Yes, DA procs 3 times in 3 Jin's swings = 6 hits TP return.

I think you'll find a number of people on these boards who would argue that while Dual Wielding, Jin can only DA twice. I can't seem to find the thread anymore, but I've never been good /w the search function.

[BerenTebogo]

I'm one of those people, if Jin could DA 3x I think it was Aurik who said in a merit pt, at the average swing rate, you would see 6-7 3x DA per hour at birds, yet I've never seen one, ever.

[eva00r]

I'm one of those people, if Jin could DA 3x I think it was Aurik who said in a merit pt, at the average swing rate, you would see 6-7 3x DA per hour at birds, yet I've never seen one, ever.

Hmm ... Ok. so don't take my answer yet then. I still need to prove this fact somehow, let me do it tomorrow. The information that I stated earlier was from what I recalled.

[Suiram]

My strongly-held belief is that Vorpal Blade single-wielded can only DA once. My somewhat-more-weakly-held belief is that the DA can occur on any hit, and then is prevented on any subsequent hits, rather than that only the initial hit has an opportunity to DA as some have conjectured.

I don't have any opinion on other weaponskills, as I've never personally collected data on them, and consider it well within the realm of possibility that they are treated differently when it comes to multiple DA/TA procs. As for those who would claim they've had multiple DA procs on single-wielded Vorpal Blade specifically, while I can't outright dismiss that possibility either (such is the nature of inductive knowledge), I feel that I've seen sufficiently many instances of it not occurring to where I would require screenshot evidence against a non-aggressive target (Fortifications or Lebros walls) to be dissuaded of this belief (I will also accept screenshots of Nidhogg popping immediately after a server maintenance).

But since this is your WS calculator, it doesn't much matter what Sath or I think can happen, so much as what you think can, or if you're unsure you could make several calculations for each possibility and then perform tests to compare the predicted numbers against the actual numbers; I think people would likely be interested in seeing that if you did.

[Max™]

I don't think DA/TA's kick off of hits in the WS.

I think the DA/TA is factored for the WS as a whole, and the max additional DA/TA's possible is capped at 2.

When I use Warrior's Charge, why should it care which swing in the WS it fires in? it just adds a hit to the WS, when I Warrior's Charge and get a Double proc, it adds two hits, naturally it checks the acc for them and all, but it's not deciding that the 2nd hit fired the DA I don't think.

Not the first either, cause of the 4% Returns I've gotten (incidentally, never seen a 5%, which would indicate more than 2 DA's) on several occasions.

I think it rolls it as the WS calculation starts.

DA1 *random number* No
DA2 *random number* Yes
ACC check swing1 through WS count +2 DA or TA's *random number* 4 Hits
WS Dmg calculation+Tp return sent back
Soandso WSes whatever it was for Thatmuch points of damage.


Why think that? Because I have to fire WC before I WS to make the WS double for sure.